Ordered sets: an introduction with connections from combinatorics to topology
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Basel]
Birkhäuser
[2016]
|
| Ausgabe: | Second edition |
| Schlagworte: | |
| Online-Zugang: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XVI, 420 Seiten, 53 illus., 10 illus. in color) |
| ISBN: | 9783319297880 |
| DOI: | 10.1007/978-3-319-29788-0 |
Internformat
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| 100 | 1 | |a Schröder, Bernd S. W. |d 1966- |e Verfasser |0 (DE-588)135918871 |4 aut | |
| 245 | 1 | 0 | |a Ordered sets |b an introduction with connections from combinatorics to topology |c Bernd Schröder |
| 250 | |a Second edition | ||
| 264 | 1 | |a [Basel] |b Birkhäuser |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a 1 Online-Ressource (XVI, 420 Seiten, 53 illus., 10 illus. in color) | ||
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| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Ordered algebraic structures | |
| 650 | 4 | |a Mathematical logic | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Mathematical Logic and Foundations | |
| 650 | 4 | |a Order, Lattices, Ordered Algebraic Structures | |
| 650 | 4 | |a Algebraic Topology | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
| _version_ | 1804176261283577856 |
|---|---|
| adam_text | ORDERED SETS
/ SCHROEDER, BERND
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
BASICS
CHAINS, ANTICHAINS, AND FENCES
UPPER AND LOWER BOUNDS
RETRACTIONS
CONSTRAINT SATISFACTION PROBLEMS
GRAPHS AND HOMOMORPHISMS
LEXICOGRAPHIC SUMS
LATTICES
TRUNCATED LATTICES
DIMENSION
INTERVAL ORDERS
SETS P^Q = HOM (Q, P) AND PRODUCTS
ENUMERATION OF ORDERED SETS
APPENDIX A: SOME ALGEBRAIC TOPOLOGY
APPENDIX B: SOME DISCRETE MORSE THEORY
REFERENCES
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ORDERED SETS
/ SCHROEDER, BERND
: 2016
ABSTRACT / INHALTSTEXT
THE SECOND EDITION OF THIS HIGHLY PRAISED TEXTBOOK PROVIDES AN EXPANDED
INTRODUCTION TO THE THEORY OF ORDERED SETS AND ITS CONNECTIONS TO
VARIOUS SUBJECTS. UTILIZING A MODULAR PRESENTATION, THE CORE MATERIAL IS
PURPOSELY KEPT BRIEF, ALLOWING FOR THE BENEFITS OF A BROAD EXPOSURE TO
THE SUBJECT WITHOUT THE RISK OF OVERLOADING THE READER WITH TOO MUCH
INFORMATION ALL AT ONCE. THE REMAINING CHAPTERS CAN THEN BE READ IN
ALMOST ANY ORDER, GIVING THE TEXT A GREATER DEPTH AND FLEXIBILITY OF
USE. MOST TOPICS ARE INTRODUCED BY EXAMINING HOW THEY RELATE TO RESEARCH
PROBLEMS, SOME OF THEM STILL OPEN, ALLOWING FOR CONTINUITY AMONG DIVERSE
TOPICS AND ENCOURAGING READERS TO EXPLORE THESE PROBLEMS FURTHER WITH
RESEARCH OF THEIR OWN. A WIDE RANGE OF MATERIAL IS PRESENTED, FROM
CLASSICAL RESULTS SUCH AS DILWORTH S, SZPILRAJN S, AND HASHIMOTO S
THEOREMS TO MORE RECENT RESULTS SUCH AS THE LI-MILNER STRUCTURE
THEOREM.MAJOR TOPICS COVERED INCLUDE CHAINS AND ANTICHAINS, LOWEST UPPER
AND GREATEST LOWER BOUNDS, RETRACTIONS, ALGORITHMIC APPROACHES,
LATTICES, THE DIMENSION OF ORDERED SETS, INTERVAL ORDERS, LEXICOGRAPHIC
SUMS, PRODUCTS, ENUMERATION, AND THE ROLE OF ALGEBRAIC TOPOLOGY. THIS
NEW EDITION SHIFTS THE PRIMARY FOCUS TO FINITE ORDERED SETS, WITH
RESULTS ON INFINITE ORDERED SETS PRESENTED TOWARD THE END OF EACH
CHAPTER WHENEVER POSSIBLE. ALSO NEW ARE CHAPTER 6 ON GRAPHS AND
HOMOMORPHISMS, WHICH SERVES TO SEPARATE THE FIXED CLIQUE PROPERTY FROM
THE MORE FUNDAMENTAL FIXED SIMPLEX PROPERTY AS WELL AS TO DISCUSS THE
CONNECTIONS AND DIFFERENCES BETWEEN GRAPH HOMOMORPHISMS AND
ORDER-PRESERVING MAPS, AND AN APPENDIX ON DISCRETE MORSE FUNCTIONS AND
THEIR USE FOR THE FIXED POINT PROPERTY FOR ORDERED SETS. RICH IN
EXAMPLES, DIAGRAMS, AND EXERCISES, THE SECOND EDITION OF ORDERED SETS
WILL BE AN EXCELLENT TEXT FOR UNDERGRADUATE AND GRADUATE STUDENTS AND A
VALUABLE RESOURCE FOR INTERESTED RESEARCHERS.IT WILL BE ESPECIALLY
USEFUL TO THOSE LOOKING FOR AN INTRODUCTION TO THE THEORY OF ORDERED
SETS AND ITS CONNECTIONS TO SUCH AREAS AS ALGEBRAIC TOPOLOGY, ANALYSIS,
AND COMPUTER SCIENCE. PRAISE FOR THE FIRST EDITION THE AUTHOR HAS DONE
THE FIELD A SERVICE BY PRODUCING AN EXCELLENT TEXT STRONG IN THE
PRESENTATION OF CERTAIN TOPOLOGICAL ASPECTS OF THE UNDERLYING DIAGRAMS,
E.G., WHICH SHOULD SERVE THE DEVELOPING COMMUNITY AND FIELD WELL AND
WHICH CAN BE RECOMMENDED WITHOUT RESERVATIONS AS ONE OF THE VOLUMES
WHICH SHOULD GRACE A POSETEER S LIBRARY WHETHER SHE IS INTERESTED ONLY
OR MAINLY IN THE THEORY OF THESE OBJECTS OR HAS DIRECTED HER GAZE
TOWARDS APPLICATIONS. AS A SOURCEBOOK OF IDEAS AND UNDERSTANDING IT WILL
MAKE ITS MARK. AND DESERVEDLY SO. — ZENTRALBLATT MATH “…A GEM.
UNDERGRADUATE MATHEMATICS AND COMPUTER SCIENCE MAJORS WILL FIND THE
FIRST CHAPTERS OFFERING BACKGROUND THAT WILL SERVE THEM WELL IN MANY
COURSES.THE REST OF THE BOOK, WHICH FEATURES MANY OPEN PROBLEMS,
CONSTITUTES AN ACCESSIBLE AND STIMULATING INVITATION TO RESEARCH . . .
HIGHLY RECOMMENDED. — CHOICE “THE AUTHOR PRESENTS THE FIELD OF
ORDERED SETS IN AN ATTRACTIVE WAY AND THE MANY OPEN PROBLEMS PRESENTED
IN THE BOOK ARE INVALUABLE...[T]HE BOOK IS A SUCCESS, IT PRESENTS AN IN
DEPTH AND UP TO DATE CAREFULLY WRITTEN COVERAGE OF ORDERED SETS.
—SIGACT NEWS.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Schröder, Bernd S. W. 1966- |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-29788-0 |
| edition | Second edition |
| format | Electronic eBook |
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| isbn | 9783319297880 |
| language | English |
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| spelling | Schröder, Bernd S. W. 1966- Verfasser (DE-588)135918871 aut Ordered sets an introduction with connections from combinatorics to topology Bernd Schröder Second edition [Basel] Birkhäuser [2016] © 2016 1 Online-Ressource (XVI, 420 Seiten, 53 illus., 10 illus. in color) txt rdacontent c rdamedia cr rdacarrier Mathematics Algebra Ordered algebraic structures Mathematical logic Algebraic topology Combinatorics Mathematical Logic and Foundations Order, Lattices, Ordered Algebraic Structures Algebraic Topology Mathematik Erscheint auch als Druckausgabe 978-3-319-29786-6 https://doi.org/10.1007/978-3-319-29788-0 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994389&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028994389&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Schröder, Bernd S. W. 1966- Ordered sets an introduction with connections from combinatorics to topology Mathematics Algebra Ordered algebraic structures Mathematical logic Algebraic topology Combinatorics Mathematical Logic and Foundations Order, Lattices, Ordered Algebraic Structures Algebraic Topology Mathematik |
| title | Ordered sets an introduction with connections from combinatorics to topology |
| title_auth | Ordered sets an introduction with connections from combinatorics to topology |
| title_exact_search | Ordered sets an introduction with connections from combinatorics to topology |
| title_full | Ordered sets an introduction with connections from combinatorics to topology Bernd Schröder |
| title_fullStr | Ordered sets an introduction with connections from combinatorics to topology Bernd Schröder |
| title_full_unstemmed | Ordered sets an introduction with connections from combinatorics to topology Bernd Schröder |
| title_short | Ordered sets |
| title_sort | ordered sets an introduction with connections from combinatorics to topology |
| title_sub | an introduction with connections from combinatorics to topology |
| topic | Mathematics Algebra Ordered algebraic structures Mathematical logic Algebraic topology Combinatorics Mathematical Logic and Foundations Order, Lattices, Ordered Algebraic Structures Algebraic Topology Mathematik |
| topic_facet | Mathematics Algebra Ordered algebraic structures Mathematical logic Algebraic topology Combinatorics Mathematical Logic and Foundations Order, Lattices, Ordered Algebraic Structures Algebraic Topology Mathematik |
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